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Imagine that wee have 10 indexed blockchain. Now, I start mining for index 11 block referencing index10's hash, I mean, the last hash data. Also, other miners starts too.

When other miner finishes mining and won the race for index11 block mining, is it normal decision for me to give up current working mining (for index11) and start mining for index 12 block referencing newly added index11 block hash?

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Yes.

Once they receive a new block and find it valid, other miners will immediately stop existing work and restart with the new block as the basis for their work. Anything else would be throwing money away pointlessly.

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